There appears to be some confusion between the Last Ship and the White Ship, on which the Keepers of the Three Rings sailed into the West. Some sources (and notably the movie version of the The Return of the King) refer to the 'Last Ship' as that used by Gandalf and his associates. If that really had been the literal 'last ship', it would have left a considerable number of Elves stranded in Middle-earth.

Notes

1

We're not told specifically when the Last Ship sailed from the Grey Havens, but we are given a clue. In The Tale of Aragorn and Arwen (The Lord of the Rings Appendix A I (v)), we're given Aragorn's final words to Arwen. Aragorn suggests that Arwen might still sail into the West, and one of the reasons she gives that this is impossible is that 'There is now no ship that would bear me hence...'. The clear implication is that the Last Ship had already sailed by IV 120, the year in which this conversation took place.

2

Strictly, it's never stated explicitly that Círdan planned to sail aboard the Last Ship, but it's twice said that he would no longer dwell at the Grey Havens after the ship sailed, which strongly implies that he intended to sail on that ship.